When dredging, a cutter head is set into material at a bottom of a body of water and is moved through the material. The speed at which the cutter head moves through the material is critical. If the cutter head moves too aggressively through the material, the cuttings produced will plug cutting discharge lines. On the other hand, if the cutter head moves too slowly through the material, the cutter head will be largely ineffective and a fluidizing stream carrying the cuttings through the discharge lines will be largely water. The problem is made more complex by a wide range of soils, which react to the cutter head in different ways. At one end of the range are clay soils. A cutter head passing through clay soils will cut a clearly defined trench. At an opposite end of the range are sandy soils, which tend to collapse and flow around the cutter head. This combination of problems makes it very difficult to automate the operation of the cutter head so that a computer controller can monitor and operate the movement of the cutter head without requiring constant monitoring by human operators. What is required is a method that of automated control of movement of a cutter head of a dredging cutter.